Electric machines are utilized in a wide variety of applications. For example, hybrid/electric vehicles (HEVs) typically include an electric traction drive system that includes an alternating current (AC) electric motor which is driven by a power converter with a direct current (DC) power source, such as a storage battery. Motor windings of the AC electric motor can be coupled to inverter sub-modules of a power inverter module (PIM). Each inverter sub-module includes a pair of switches that switch in a complementary manner to perform a rapid switching function to convert the DC power to AC power. This AC power drives the AC electric motor, which in turn drives a shaft of HEV's drivetrain. Some traditional HEVs implement two three-phase pulse width modulated (PWM) inverter modules and two three-phase AC machines (e.g., AC motors) each being driven by a corresponding one of the three-phase PWM inverter modules that it is coupled to. In some systems, voltage command signals are applied to a pulse width modulation (PWM) module. The PWM module applies PWM waveforms to the phase voltage command signals to control pulse width modulation of the phase voltage command signals and generate switching vector signals that are provided to the PWM inverter module.
Many modern high performance AC motor drives use the principle of field oriented control (FOC) or “vector” control to control operation of the AC electric motor. In particular, vector control is often used in variable frequency drives to control the torque applied to the shaft (and thus the speed) of an AC electric motor by controlling the current fed to the AC electric motor. In short, stator phase currents are measured and converted into a corresponding complex space vector. This current vector is then transformed to a coordinate system rotating with the rotor of the AC electric motor.
Recently, researchers have used multi-phase machines in various applications including electric vehicles. As used herein, the term “multi-phase” refers to two or more phases, and can be used to refer to electric machines that have two or more phases. A multi-phase electric machine typically includes a multi-phase PWM inverter module that drives one or more multi-phase AC machine(s). One example of such a multi-phase electric machine is a three-phase AC machine. In a three-phase system, a three-phase PWM inverter module drives one or more three-phase AC machine(s).
In such multi-phase systems, voltage command signals are applied to a pulse width modulation (PWM) module. To control pulse width modulation of the voltage command signals, the PWM module applies PWM waveforms. The PWM waveforms that have a controllable duty cycle with a variable PWM period, to the voltage command signals to generate switching vector signals that are provided to the PWM inverter module. A modulation index, which is defined as a normalized fundamental reference voltage, can be used to characterize performance of the PWM. The modulation index is the ratio of the peak fundamental phase voltage (Vr) to the maximum available voltage. In a three-phase system, three important modulation regions can be defined in terms of their modulation index. The regions are defined as a linear modulation region, a first overmodulation region, and a second overmodulation region. For a three-phase machine operating in the linear modulation region, the modulation index ranges between zero and 0.9069 as described in expression (1A) as follows:
                              MI          ∈                      [                          0              ,                              π                                  2                  ⁢                                      3                                                                        ]                          =                              [                          0              ,              0.9069                        ]                    .                                    (                  1          ⁢          A                )            
Similarly, for a five-phase machine, the linear modulation region the modulation index ranges between zero and 0.9669 as described in expression (1B) as follows:
                              MI          ∈                      [                          0              ,                                                π                  ⁢                                                            5                      +                                              2                        ⁢                                                  5                                                                                                                    10                                      ]                          =                              [                          0              ,              0.9669                        ]                    .                                    (                  1          ⁢          B                )            
For a three-phase machine operating in the first overmodulation region the modulation index ranges between 0.9069 and 0.9514 as described in expression (2A) as follows:
                              MI          ∈                      [                                          π                                  2                  ⁢                                      3                                                              ,                                                                    3                                    2                                ⁢                ln                ⁢                                                                  ⁢                3                                      ]                          =                              [                          0.9069              ,              0.9514                        ]                    .                                    (                  2          ⁢          A                )            
Similarly, for a five-phase machine operating in the first overmodulation region, the modulation index ranges between 0.9669 and 0.9832 as described in expression (2B) as follows:
                              MI          ∈                                                    π                ⁢                                                      5                    +                                          2                      ⁢                                              5                                                                                                        10                        ⁡                          [                              1                ,                                                      5                    π                                    ⁢                                      ln                    ⁡                                          (                                                                        2                          +                                                      5                                                                                                    5                                                                    )                                                                                  ]                                      =                              [                          0.9699              ,              0.9832                        ]                    .                                    (                  2          ⁢          B                )            
For a three-phase machine operating in the second overmodulation region the modulation index ranges between 0.9514 and 1.0000 as described in expression (3A) as follows:MIε[0.9514,1]  (3A).
Similarly, for a five-phase machine operating in the second overmodulation region, the modulation index ranges between 0.9832 and 1.0000 as described in expression (3B) as follows:MIε[0.9832,1]  (3B).
When the multi-phase machine is operating at between medium to high speed, this operating mode is commonly referred to as being in either a first overmodulation region or second overmodulation region. Performance of inverter modules in the second overmodulation region could be limited by hard limit of modulation index to less than 100%. As a consequence, the stator voltages that can be generated are less than 100% of the maximum available voltage, and the maximum torque that can be generated is therefore also less than 100%.
To address this issue, overmodulation methods have been developed for modifying the stationary reference frame voltage command signals. However, existing methods used to generate these modified voltage command signals can generate a discontinuity when the system operates in an overmodulation region. This can be seen in the stationary reference frame β-axis voltage command signal (Vβ**), and eventually results in an asymmetric duty cycles for the phase voltage command signals (Vbs*, Vcs*) for phases B and C. As a result, the wrong phase voltages are applied to phase B and C, which negatively affects control of the current regulator and field-weakening loop. For example, if the wrong phase voltage is applied to the machine, phase current may not be properly regulated, which may in turn cause current/torque oscillations.
It would be desirable to provide a mechanism for ensuring that the correct phase voltages are generated and applied to a multi-phase machine to help maintain proper phase current regulation when operating in the overmodulation region(s). Other desirable features and characteristics of the present invention will become apparent from the subsequent detailed description and the appended claims, taken in conjunction with the accompanying drawings and the foregoing technical field and background.